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In the asymptotic setting of change-point estimation the behavior of the posterior distribution and of Bayes procedures is studied. The limiting distribution is derived when the prior probabilities converge to geometric probabilities. This distribution is related to the infinite product of random matrices (or affine transforms of the real line). The situation with partially unknown pre- and after-change distributions is investigated. A condition for the limiting law of posterior probabilities to coincide with that for the known pre- and after-change distributions is derived.